Geometric Algorithm for Multiparametric Linear Programming

F. Borrelli, A. Bemporad and M. Morari
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F. Borrelli: Swiss Federal Institute of Technology, ETH
A. Bemporad: Universita di Siena
M. Morari: Swiss Federal Institute of Technology, ETH

Journal of Optimization Theory and Applications, 2003, vol. 118, issue 3, No 3, 515-540

Abstract: Abstract We propose a novel algorithm for solving multiparametric linear programming problems. Rather than visiting different bases of the associated LP tableau, we follow a geometric approach based on the direct exploration of the parameter space. The resulting algorithm has computational advantages, namely the simplicity of its implementation in a recursive form and an efficient handling of primal and dual degeneracy. Illustrative examples describe the approach throughout the paper. The algorithm is used to solve finite-time constrained optimal control problems for discrete-time linear dynamical systems.

Keywords: Multiparametric programming; sensitivity analysis; postoptimality analysis; linear programming; optimal control (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (15)

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DOI: 10.1023/B:JOTA.0000004869.66331.5c

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